Nonlinear Fokker-Planck Equation in the Model of Asset Returns
Abstract
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker-Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leading term of the Cauchy problem solution asymptotic in a formal small parameter in semiclassical approximation following the complex WKB-Maslov method in the class of trajectory concentrated functions.
Keywords
Cite
@article{arxiv.0804.0900,
title = {Nonlinear Fokker-Planck Equation in the Model of Asset Returns},
author = {Alexander Shapovalov and Andrey Trifonov and Elena Masalova},
journal= {arXiv preprint arXiv:0804.0900},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/